• Cathode rays (Thomson): streams of negative particles, identical whatever the gas or electrode metal. They travel in straight lines, carry momentum and are deflected by electric and magnetic fields towards the positive plate.
• Positive rays (canal rays): their charge-to-mass ratio depends on the gas in the tube. The lightest, from hydrogen, is the proton.
• Rutherford's gold-foil experiment: most α-particles pass straight through, a few are deflected strongly. So the atom is mostly empty space, with a tiny, dense, positive nucleus.
• Radioactivity was discovered by Becquerel. Neutrons were identified later (Chadwick).

Z = number of protons, and A = protons + neutrons. Isotopes have the same Z but different A. The atomic mass unit is 1/12 of the mass of a ¹²C atom. Relative atomic mass is the abundance-weighted mean of the isotope masses.

Light behaves as a wave (c = νλ) and as a stream of photons (E = hν). Matter also has wave character: λ = h/mv (de Broglie). Energy in atoms is quantised, so electrons can only occupy fixed energy levels.

Each line comes from an electron falling from a higher level to a lower one: ΔE = hν. The Lyman series ends on n = 1 (ultraviolet). The Balmer series ends on n = 2 (visible). The Paschen series ends on n = 3 (infrared). Lines crowd together at high frequency because the levels converge.

A sub-shell has 2l + 1 orbitals. A shell holds up to 2n² electrons. Each orbital holds at most two electrons, with opposite spins.

The Aufbau principle fills orbitals from lowest energy upwards: 1s 2s 2p 3s 3p 4s 3d 4p. The Pauli principle allows no two electrons the same four quantum numbers. Hund's rule puts one electron in each orbital of a sub-shell, with parallel spins, before any pairing.

Learn the exceptions: Cr is [Ar]3d⁵4s¹ and Cu is [Ar]3d¹⁰4s¹. Transition metals lose their 4s electrons before 3d electrons when they form ions (Fe³⁺ = [Ar]3d⁵).

• Atomic radius decreases across a period, because effective nuclear charge rises while shielding barely changes. It increases down a group.
• Isoelectronic ions: the more protons, the smaller the ion. So O²⁻ > F⁻ > Na⁺ > Mg²⁺.
• First ionization energy rises across a period, but dips at Group 13 (a 2p electron is higher in energy) and at Group 16 (repulsion between paired electrons).
• Successive ionization energies jump sharply when an electron must come from a new, inner shell. The jump tells you the group.
• Electron gain energy becomes more negative across a period. Cl is more negative than F because F is small and crowded. N and the noble gases have positive or near-zero values.
• Electronegativity increases across a period and decreases down a group. F is the highest.

Count all the valence electrons, add one for each negative charge and remove one for each positive charge. Join the atoms with single bonds, complete the octets of the outer atoms, then put any remaining electrons on the central atom. Period 3 and heavier central atoms (P, S, Cl, Xe) can exceed an octet. B and Be can have fewer than eight.

Formal charge = (valence electrons) − (non-bonding electrons) − ½(bonding electrons). The most acceptable structure has the smallest formal charges, puts any negative formal charge on the more electronegative atom, and avoids like charges on neighbouring atoms.

Both bonding electrons come from one atom, for example NH₄⁺, H₃O⁺, H₃N→BF₃ and CO. Once a dative bond has formed, it is identical to any other covalent bond.

Repulsion decreases in the order lone pair–lone pair > lone pair–bond pair > bond pair–bond pair, so lone pairs squeeze bond angles (CH₄ 109.5°, NH₃ 107°, H₂O 104.5°). NF₃ has a smaller angle than NH₃ because the bonding pairs are pulled out towards F. In a trigonal bipyramid, lone pairs sit in the equatorial positions.

sp (180°), sp² (120°), sp³ (109.5°), sp³d (trigonal bipyramidal) and sp³d² (octahedral). A double bond is one σ bond plus one π bond. A triple bond is one σ plus two π. σ bonds form from end-on overlap (s–s, s–hybrid, hybrid–hybrid). π bonds form from sideways overlap of p orbitals. Paper II often asks which orbitals overlap to form a named bond.

When one Lewis structure cannot describe a species, the real structure is a resonance hybrid of several contributing structures (NO₃⁻, CO₃²⁻, O₃, C₆H₆, carboxylate ions). The bonds are equal in length and intermediate between single and double. Only electrons move between resonance structures, never atoms. The most stable contributors have complete octets, fewer separated charges and negative charge on the more electronegative atom.

A polar bond does not guarantee a polar molecule. The bond dipoles may cancel by symmetry (CO₂, BF₃, CCl₄ and SF₆ are non-polar; SO₂, NF₃ and SF₄ are polar). The electronegativity of an atom also depends on its hybridization (sp C > sp² C > sp³ C) and on its oxidation state and charge. A carbon bonded to more electronegative atoms is itself more electronegative.

• Covalent character in ionic compounds increases with the polarizing power of the cation (small and highly charged) and the polarizability of the anion (large).
• Metallic bonding becomes stronger with more delocalised electrons per atom and smaller atoms. Group 2 metals have stronger bonding than Group 1.
• Secondary interactions include ion–dipole, dipole–dipole, hydrogen bonding (H on N, O or F) and London dispersion forces, which grow with molar mass and surface area. They control boiling points and solubility.

Elements are 0. O is usually −2 (−1 in peroxides). H is +1 (−1 in metal hydrides). F is always −1. The oxidation numbers in a species add up to its charge. Oxidation is an increase in oxidation number (loss of electrons) and reduction is a decrease. In a disproportionation, one element is oxidized and reduced at the same time (for example Cl₂ + H₂O).

Use Stock notation for variable valency, such as iron(III) chloride. Learn the polyatomic ions: NO₃⁻, NO₂⁻, SO₄²⁻, SO₃²⁻, S₂O₃²⁻, CO₃²⁻, HCO₃⁻, PO₄³⁻, MnO₄⁻, CrO₄²⁻, Cr₂O₇²⁻, ClO⁻, ClO₃⁻ and ClO₄⁻.

n = m/M and N = n × N_A (6.022 × 10²³ mol⁻¹). An empirical formula comes from the mole ratio of the elements. The molecular formula = (empirical formula) × (M ÷ empirical formula mass).

• Mass fraction, %(w/w), %(w/v) and mole fraction x_i = n_i/n_total.
• Molarity is mol dm⁻³ of solution. Molality is mol kg⁻¹ of solvent. ppm is mg kg⁻¹ (≈ mg dm⁻³ for dilute water).
• Concentration of a commercial acid: c = (1000 × d × w%) ÷ (100 × M), with d in g cm⁻³.

Simple equations can be balanced by inspection. For redox equations, balance the electron change: write the oxidation and reduction half-equations, balance O with H₂O and H with H⁺, then the charge with electrons, and combine. Nuclear equations must balance mass number and atomic number.

Dilution: c₁V₁ = c₂V₂. Use a primary standard to make a standard solution. Limiting reagent, percentage yield, gas volumes and titrations (acid–base, KMnO₄, K₂Cr₂O₇, iodometric with Na₂S₂O₃) all come back to the mole ratio in the balanced equation.

Boyle's law: PV is constant (fixed n and T). Charles's law: V ∝ T (fixed n and P). Avogadro's law: V ∝ n. Together these give PV = nRT, with P in Pa, V in m³, T in K and R = 8.314 J K⁻¹ mol⁻¹. The molar volume of any ideal gas at 273 K and 1 atm is 22.4 dm³ mol⁻¹. Rearranging gives M = ρRT/P.

P_total = P_A + P_B + …, and each partial pressure P_A = x_A P_total. In a rigid container V is fixed, so the pressure is proportional to nT. Watch the total number of gas moles change as a reaction goes on.

The model assumes negligible molecular volume, no intermolecular forces, elastic collisions and random motion. It gives PV = ⅓Nmc², where c² is the mean square speed. The average kinetic energy depends only on temperature: any two gases at the same T have the same average kinetic energy. c_rms = √(3RT/M), so lighter molecules move faster.

Raising the temperature flattens and broadens the curve and moves the peak to higher speed. The area under the curve, which is the number of molecules, stays the same. More molecules now exceed any chosen energy, and this links straight to reaction rates in Unit 11.

Real gases deviate from ideal behaviour at high pressure (molecular volume matters) and low temperature (attractions matter). Gases are most nearly ideal at low pressure and high temperature. The compressibility factor Z = PV/nRT. The van der Waals equation is (P + an²/V²)(V − nb) = nRT. Above its critical temperature, a gas cannot be liquefied by pressure alone.

A system can be open (exchanges matter and energy), closed (exchanges energy only) or isolated (exchanges neither). Enthalpy H, entropy S and Gibbs energy G are state functions: a change in any of them depends only on the initial and final states, not on the route.

ΔH is the heat change at constant pressure. Exothermic means ΔH < 0 and endothermic means ΔH > 0. Learn the standard enthalpies of formation, combustion, neutralization, solution, hydration, atomization, bond dissociation, ionization and electron gain. Each definition names the substance, the amount (1 mol) and the physical states.

Hess's law: the total enthalpy change is the same whatever route is taken. Calorimetry gives q = mcΔT, and ΔH = −q/n.

• From formation data: ΔH_r = ΣΔH_f(products) − ΣΔH_f(reactants).
• From combustion data: ΔH_r = ΣΔH_c(reactants) − ΣΔH_c(products).
• From bond enthalpies (gases only): ΔH_r = Σ(bonds broken) − Σ(bonds formed).

ΔH_f(MX) = ΔH_atom(M) + IE + ΔH_atom(X) + electron gain energy + lattice enthalpy (the formation of the solid lattice from gaseous ions, which is negative). The magnitude of the lattice enthalpy increases with higher ionic charges and smaller ions. Enthalpy of solution = (lattice dissociation enthalpy) + Σ(hydration enthalpies of the ions).

Entropy measures how widely energy and matter are dispersed: S(solid) < S(liquid) < S(gas). Entropy increases when a gas forms, when moles of gas increase, when a solid dissolves, and when temperature rises. For the surroundings, ΔS_surr = −ΔH/T.

ΔG = ΔH − TΔS. A process is spontaneous when ΔG < 0. At a phase change, ΔG = 0, so T = ΔH/ΔS (for example, the boiling point is ΔH_vap/ΔS_vap).

Reactivity increases down the group. 2M + 2H₂O → 2MOH + H₂. On burning in air, Li forms Li₂O, Na forms Na₂O₂ (peroxide) and K forms KO₂ (superoxide). Li is the only Group 1 metal that forms a nitride (Li₃N). LiNO₃ and Li₂CO₃ decompose like Group 2 salts (diagonal relationship with Mg). Other Group 1 carbonates are stable, and their nitrates give the nitrite plus O₂. Almost all Group 1 salts are soluble. Flame colours: Li crimson, Na yellow, K lilac.

Be is amphoteric. Mg reacts with steam, while Ca, Sr and Ba react with cold water. When burnt in air they also form nitrides (Mg₃N₂). The thermal stability of carbonates and nitrates increases down the group, because the polarizing power of the cation decreases. Hydroxides become more soluble down the group, and sulfates become less soluble (BaSO₄ is insoluble). Flame colours: Ca brick-red, Sr crimson, Ba apple-green. Mg gives no flame colour.

Al: Al₂O₃ and Al(OH)₃ are amphoteric and dissolve in excess NaOH as [Al(OH)₄]⁻. AlCl₃ is covalent, forms the dimer Al₂Cl₆, acts as a Lewis acid (as in Friedel–Crafts) and hydrolyses to give an acidic solution. Concentrated HNO₃ makes Al passive. C: diamond (sp³, hard, an insulator) and graphite (sp² layers, conducts). CO is a neutral, toxic reducing agent. CO₂ is acidic and forms H₂CO₃ in water.

N₂ is unreactive because of its strong triple bond. NH₃ is basic, acts as a ligand and is made by the Haber process. Ammonium salts release NH₃ when warmed with NaOH. On heating: NH₄NO₃ → N₂O + 2H₂O, NH₄NO₂ → N₂ + 2H₂O, (NH₄)₂Cr₂O₇ → N₂ + Cr₂O₃ + 4H₂O. HNO₃ is an oxidizing acid: concentrated acid with Cu gives NO₂, dilute acid gives NO. Concentrated HNO₃ is kept in brown bottles because light decomposes it to NO₂.

The allotropes are O₂ and O₃ (ozone has a pungent smell). H₂O boils far higher than H₂S because of hydrogen bonding. H₂O₂ can act as an oxidizing agent or a reducing agent (it reduces MnO₄⁻), and it decomposes to H₂O + O₂, catalysed by MnO₂. Rhombic sulfur is the stable allotrope at room temperature. SO₂ is a reducing agent: it turns acidified Cr₂O₇²⁻ from orange to green and decolourises MnO₄⁻. Concentrated H₂SO₄ is both a dehydrating agent and an oxidizing agent. S₂O₃²⁻ + 2H⁺ → S + SO₂ + H₂O.

Oxidizing power: F₂ > Cl₂ > Br₂ > I₂. In water, HF is a weak acid, while HCl, HBr and HI are strong. Acid strength increases from HCl to HI as the H–X bond weakens. HF has the highest boiling point of the hydrogen halides (hydrogen bonding). Cl₂ + H₂O → HCl + HOCl is a disproportionation. With cold dilute NaOH, Cl₂ gives NaCl + NaOCl. With hot concentrated NaOH, it gives NaCl + NaClO₃. Acid strength of the chlorine oxoacids increases from HOCl to HClO₄. Xenon compounds: XeF₂ (linear), XeF₄ (square planar), XeO₃ (trigonal pyramidal).

Oxides go from basic (Na₂O, MgO) through amphoteric (Al₂O₃) to acidic (SiO₂, P₄O₁₀, SO₃, Cl₂O₇). NaCl and MgCl₂ are ionic. AlCl₃, SiCl₄ and PCl₅ hydrolyse in water to give acidic solutions.

They show variable oxidation states, coloured ions (from d–d transitions in partly filled d orbitals), catalytic activity (Fe in the Haber process, V₂O₅ in the Contact process, Ni in hydrogenation) and complex formation. Sc³⁺ (d⁰) and Zn²⁺ (d¹⁰) are colourless, and Zn has the lowest melting point in the 3d series. Oxides become more acidic as the oxidation state rises: CrO is basic, Cr₂O₃ amphoteric and CrO₃ acidic; MnO is basic and Mn₂O₇ acidic. 2CrO₄²⁻ (yellow) + 2H⁺ ⇌ Cr₂O₇²⁻ (orange) + H₂O. MnO₄⁻ is reduced to Mn²⁺ in acid, MnO₂ in neutral solution and MnO₄²⁻ (green) in strong alkali.

Name the ligands in alphabetical order (ammine, aqua, chlorido, cyanido, hydroxido), with di-, tri-, tetra- and so on. Then name the metal with its oxidation state in Roman numerals, using the -ate ending for an anionic complex. For example: [Cu(NH₃)₄]²⁺ is tetraamminecopper(II); K₃[Fe(CN)₆] is potassium hexacyanidoferrate(III); [Co(NH₃)₆]Cl₃ is hexaamminecobalt(III) chloride. The colour depends on the metal, its oxidation state and the ligands. Fe³⁺ with SCN⁻ gives a blood-red colour.

Carbon is tetravalent and can form stable chains and rings (catenation) as well as single, double and triple bonds, so it builds a huge variety of structures.

The classes to know are alcohols, ethers, aldehydes, ketones, alkyl halides, carboxylic acids, acid halides, esters, amides, amines and nitriles, plus alkenes and alkynes. When a compound has several groups, the principal (suffix) group follows the priority carboxylic acid > ester > acid halide > amide > aldehyde > ketone > alcohol > amine. Halo- and nitro- groups are always prefixes.

1. Find the principal group.
2. Choose the main chain that contains it (and any C=C or C≡C).
3. Number the chain from the end that gives the principal group the lowest number, then the multiple bonds, then the substituents.
4. Put the prefixes in alphabetical order (bromo, chloro, ethyl, formyl, hydroxy, methyl, oxo …).
5. Build the name: prefixes + parent chain + -en-/-yn- + suffix.

Examples: HOCH₂CH₂CHO is 3-hydroxypropanal, and CH₃CH(Br)CH=CHCOOH is 4-bromopent-2-enoic acid.

Constitutional isomers differ in the chain, the position of a group or the functional group. Stereoisomers have the same connectivity but a different arrangement in space:

• Geometric (cis/trans): needs restricted rotation (C=C) and two different groups on each doubly bonded carbon.
• Optical: needs a chiral carbon (four different groups). Enantiomers are non-superimposable mirror images that rotate plane-polarised light equally in opposite directions. A racemic mixture is optically inactive.
• Diastereoisomers are stereoisomers that are not mirror images. Cis and trans isomers are diastereoisomers.

In light, Cl₂ → 2Cl• (initiation). Then Cl• + CH₄ → •CH₃ + HCl and •CH₃ + Cl₂ → CH₃Cl + Cl• (propagation). Two radicals combining is termination, for example •CH₃ + •CH₃ → C₂H₆. This is why ethane appears as a by-product. The reaction gives a mixture of substituted products.

• HX: H⁺ adds first to give the more stable carbocation (3° > 2° > 1°), so H goes to the carbon that already has more H (Markovnikov's rule). With peroxides, HBr adds the opposite way.
• Br₂ (in water or CCl₄): the bromine colour disappears, which is the test for C=C. The reaction goes through a cyclic bromonium ion.
• Concentrated H₂SO₄, then water: gives an alcohol (Markovnikov orientation).
• H₂ with Ni or Pd: gives the alkane. Cold, dilute alkaline KMnO₄: gives a diol, and the purple colour turns to a brown MnO₂ precipitate.

Alkynes add Br₂ and HX twice. With Hg²⁺ and dilute H₂SO₄, water adds to give an enol, which rearranges to a carbonyl compound (ethyne gives ethanal). H₂ with Lindlar's catalyst (Pd/BaSO₄/quinoline) stops at the cis-alkene. A terminal alkyne has an acidic C–H. It gives a precipitate with ammoniacal AgNO₃ (white) or ammoniacal CuCl (red), and reacts with CH₃MgBr to give RC≡CMgBr + CH₄.

Benzene is a resonance hybrid with six delocalised π electrons. All C–C bonds are equal (between single and double), and the ring is far more stable than a 'cyclohexatriene' would be. Benzene therefore undergoes substitution, not addition. Nitration uses concentrated HNO₃ and concentrated H₂SO₄ (electrophile NO₂⁺). Halogenation uses Cl₂/FeCl₃ or Br₂/FeBr₃. Friedel–Crafts alkylation uses RCl/AlCl₃, and acylation uses RCOCl/AlCl₃. The mechanism: the electrophile attacks, forming a resonance-stabilised carbocation (arenium ion), which then loses H⁺. The ring resists oxidation, but alkyl side chains are oxidized to –COOH by KMnO₄.

ortho/para directors: –OH, –NH₂, –OR and alkyl groups (activating), and halogens (deactivating). meta directors: –NO₂, –CHO, –COR, –COOH, –CN and –CO₂R (deactivating). In a synthesis, the order of steps decides which isomer you get.

The C–X bond is polar, so the carbon is attacked by nucleophiles. Aqueous NaOH gives an alcohol. KCN gives a nitrile (one carbon longer). RO⁻ gives an ether. NH₃ gives amines. Alcoholic KOH causes elimination to the more substituted alkene. Tertiary halides react by S_N1 (carbocation, rate = k[RX]), primary halides by S_N2 (one step, back-side attack, rate = k[RX][Nu⁻]). With Mg in dry ether, RX gives the Grignard reagent RMgX, which water destroys (giving RH). Aryl halides such as C₆H₅Cl do not undergo nucleophilic substitution easily.

Alcohols are classified as 1°, 2° or 3° by the carbon carrying –OH. Hydrogen bonding gives them high boiling points, and their water solubility falls as the chain grows. Breaking O–H: 2ROH + 2Na → 2RONa + H₂. Breaking C–O: PCl₅, PCl₃ or HX gives RX. Lucas reagent (ZnCl₂/conc. HCl) goes cloudy at once with 3°, after a few minutes with 2°, and not at room temperature with 1°. Concentrated H₂SO₄ and heat (or Al₂O₃) dehydrate an alcohol to an alkene. Oxidation: 1° → aldehyde (with PCC) → carboxylic acid (with acidified K₂Cr₂O₇ or KMnO₄); 2° → ketone; 3° → no reaction. Dichromate turns from orange to green.

Phenol is more acidic than an alcohol (the phenoxide ion is stabilised by resonance) but weaker than a carboxylic acid. It reacts with NaOH but not with NaHCO₃ (no CO₂). Its C–O bond does not undergo nucleophilic substitution. The ring is strongly activated: Br₂(aq) gives a white precipitate of 2,4,6-tribromophenol without a catalyst, and dilute HNO₃ nitrates it. FeCl₃ gives a violet colour.

The polar C=O group undergoes nucleophilic addition. HCN gives a cyanohydrin. A Grignard reagent gives an alcohol after hydrolysis (HCHO gives 1°, other RCHO give 2°, ketones give 3°). 2,4-DNP (Brady's reagent) gives an orange-red precipitate, which is the test for C=O. Dilute NaOH causes aldol condensation when the compound has an α-H. LiAlH₄ or NaBH₄ reduce them to alcohols, and Zn(Hg)/conc. HCl (Clemmensen) reduces C=O to CH₂. Only aldehydes are oxidized by Tollens' reagent (silver mirror), Fehling's solution (red Cu₂O) and acidified dichromate.

Hydrogen-bonded dimers give them higher boiling points than alcohols of similar mass. They liberate CO₂ from NaHCO₃. Electron-withdrawing groups make the acid stronger (ClCH₂COOH > CH₃COOH). PCl₅ gives the acid chloride. An alcohol with concentrated H₂SO₄ gives an ester (reversible). NH₃ gives the ammonium salt, which becomes an amide on heating. LiAlH₄ reduces the acid to a 1° alcohol. With a Grignard reagent, the acidic H gives an alkane.

Reactivity: acid chloride > ester > amide. Acid chlorides react with water (giving the acid), alcohols and phenols (esters), NH₃ or amines (amides) and NaOH (the carboxylate), through a tetrahedral intermediate. Esters hydrolyse in acid (reversible) or base (saponification). With excess Grignard reagent they give 3° alcohols, because the ketone formed first reacts faster than the ester. LiAlH₄ gives two alcohols. Amides hydrolyse in acid or base, and LiAlH₄ reduces them to amines.

The lone pair on N accepts H⁺. Aliphatic amines are stronger bases than NH₃ because alkyl groups release electrons. Aniline is a much weaker base because its lone pair is delocalised into the ring. Amides are practically neutral because the lone pair is delocalised onto C=O. Amines are more basic than alcohols because N is less electronegative than O. Order: ethylamine > NH₃ > aniline > ethanamide.

• With alkyl halides: a mixture of 2° and 3° amines and the quaternary ammonium salt.
• With aldehydes and ketones: an imine (C=N), formed by condensation.
• With acid chlorides: an N-substituted amide.
• With nitrous acid (NaNO₂/HCl): an aliphatic 1° amine gives an alcohol plus N₂ gas. Aniline at 0–5 °C gives benzenediazonium chloride.
• Aniline's ring is strongly activated: Br₂(aq) gives a white precipitate of 2,4,6-tribromoaniline.

C₆H₅N₂⁺Cl⁻ is stable only below about 5 °C. Replacement reactions (N₂ is released): warm water gives phenol; H₃PO₂ gives benzene; CuCl or CuBr gives chloro- or bromobenzene; CuCN gives benzonitrile (which hydrolyses to benzoic acid); KI gives iodobenzene. As an electrophile, it couples with phenol in alkaline solution to give an orange-red azo dye, and also couples with aromatic amines.

Rate is the change in concentration per unit time. It can be an average, instantaneous or initial rate. For aA + bB → cC, rate = −(1/a)Δ[A]/Δt = −(1/b)Δ[B]/Δt = (1/c)Δ[C]/Δt. So in O₂ + 2H₂ → 2H₂O, [H₂] falls twice as fast as [O₂].

Rates are followed by gas volume, pressure in a rigid container, colour (colorimetry), conductivity, or titration of quenched samples. 'Clock' reactions, such as thiosulfate with acid, measure the time to reach a fixed point. Keep the temperature constant, because rate depends strongly on T.

For a reaction to happen, particles must collide with energy ≥ E_a and with the correct orientation. Concentration and pressure raise the collision frequency. Temperature mainly raises the fraction of collisions with E ≥ E_a (the Maxwell–Boltzmann tail). Surface area and light also matter.

rate = k[A]^m[B]ⁿ. The orders m and n are found by experiment, not from the balanced equation. The units of k are mol dm⁻³ s⁻¹ (zero order), s⁻¹ (first order) and mol⁻¹ dm³ s⁻¹ (second order). Initial-rate method: change one concentration at a time. If doubling [A] doubles the rate, the order is 1. If it quadruples the rate, the order is 2. If the rate is unchanged, the order is 0.

Zero order: [A] against t is a straight line, and t_½ = [A]₀/2k. First order: ln[A] against t is a straight line, and t_½ = 0.693/k, independent of [A]₀. After n half-lives, (½)ⁿ remains, so 87.5% has reacted after 3 half-lives. When one reactant is in large excess, the reaction behaves as pseudo-first-order.

A catalyst provides an alternative pathway with a lower E_a. It speeds up the forward and reverse reactions equally. It changes neither ΔH nor the position of equilibrium, and it is regenerated at the end. Catalysts can be homogeneous or heterogeneous.

An elementary step's molecularity (1, 2 or 3) equals its order. The slowest step determines the rate. Intermediates are formed in one step and used up in a later one, whereas a catalyst is used up first and regenerated. When a fast pre-equilibrium comes before a slow step, substitute K for the intermediate: for I₂ ⇌ 2I (fast) followed by H₂ + 2I → 2HI (slow), rate = k[H₂][I₂]. An energy profile shows E_a, ΔH, transition states and any intermediates, and has one hump for each step.

K_c uses equilibrium concentrations. K_p uses partial pressures. K_p = K_c(RT)^Δn, where Δn is the change in moles of gas. Pure solids and liquids are left out (CaCO₃(s) ⇌ CaO(s) + CO₂(g) gives K_p = P_CO2). Reversing an equation gives 1/K. Multiplying an equation by n gives Kⁿ. Adding equations multiplies their K values. If Q < K the reaction moves forward, and if Q > K it moves backward.

Adding a reactant or removing a product shifts the equilibrium to the right. Raising the pressure by reducing the volume favours the side with fewer moles of gas. Raising the temperature favours the endothermic direction, and only temperature changes K. A catalyst does not shift the equilibrium. An inert gas added at constant volume has no effect. At constant pressure it favours the side with more moles of gas.

Brønsted–Lowry acids donate protons and bases accept them, forming conjugate pairs. K_w = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C, so pH + pOH = 14. K_w increases with temperature: pure water at a higher temperature has pH < 7 but is still neutral. For a weak acid: K_a = [H⁺][A⁻]/[HA], [H⁺] ≈ √(K_a c), and the degree of dissociation α ≈ √(K_a/c), which increases on dilution. For a conjugate pair, K_a × K_b = K_w.

A salt of a weak acid and strong base is basic (CH₃COONa). A salt of a weak base and strong acid is acidic (NH₄Cl). At the equivalence point: strong acid with strong base gives pH 7; weak acid with strong base gives pH > 7 (use phenolphthalein); weak base with strong acid gives pH < 7 (use methyl orange). At half-equivalence in a weak-acid titration, pH = pK_a. For a diprotic acid such as H₂CO₃, K_a1 ≫ K_a2.

A buffer is a weak acid with its salt, or a weak base with its salt. pH = pK_a + log([A⁻]/[HA]). Added H⁺ is removed by A⁻, and added OH⁻ is removed by HA. The buffer works best when [A⁻] = [HA], where pH = pK_a.

For AB, K_sp = s². For AB₂ or A₂B, K_sp = 4s³. A precipitate forms when the ionic product exceeds K_sp. A common ion lowers solubility. Salts whose anion is a weak base (OH⁻, CO₃²⁻, C₂O₄²⁻, S²⁻) are more soluble in acid. When two precipitates are possible, the one whose K_sp is reached first forms first, which is the basis of selective precipitation and of H₂S group separation (Unit 6). AgBr turns into AgI when I⁻ is added, because AgI has the smaller K_sp.

The saturated vapour pressure depends only on temperature, not on the amount of liquid or the volume. A liquid boils when its vapour pressure equals the external pressure, so water boils below 100 °C at low pressure. In a phase diagram, know the triple point and the critical point. Water's solid–liquid line slopes backwards, so ice melts under pressure. CO₂'s triple point is above 1 atm, so dry ice sublimes.

Raoult's law: P_A = x_A P_A°. An ideal mixture has ΔH_mix = 0 and ΔV_mix = 0, because A–B forces equal the A–A and B–B forces. The vapour is richer in the more volatile component, which is the basis of fractional distillation. Positive deviation gives a minimum-boiling azeotrope, and negative deviation a maximum-boiling one. Immiscible liquids each exert their full vapour pressure, so the mixture boils below either pure liquid: this is steam distillation (used for essential oils). Partition coefficient K_D = [X]_org/[X]_aq at a fixed temperature, for the same molecular form. Several small extractions remove more than one large one.

Electrolyte solutions conduct through moving ions. Conductivity rises with ionic charge, ion mobility (H⁺ and OH⁻ are exceptionally mobile), concentration and temperature. Molar conductivity Λ_m = κ/c. For a strong electrolyte it falls slightly as concentration rises. For a weak electrolyte it rises sharply on dilution, because the degree of dissociation increases.

• Metal / metal ion, such as Zn²⁺(aq)/Zn(s).
• Metal / insoluble salt, such as Ag(s)/AgCl(s)/Cl⁻(aq) and calomel Hg(l)/Hg₂Cl₂(s)/Cl⁻(aq). Their potential depends on [Cl⁻].
• Gas electrode: the standard hydrogen electrode (Pt, H₂ at 1 atm, [H⁺] = 1 mol dm⁻³, 25 °C) is defined as E° = 0.00 V.
• Redox electrode: Pt in Fe³⁺/Fe²⁺, or in MnO₄⁻/Mn²⁺/H⁺.

The electrode potential depends on concentration and temperature (and on pressure for gas electrodes), but not on electrode size or solution volume.

The anode is where oxidation happens (the negative electrode). The cathode is where reduction happens (positive). Electrons flow through the wire from anode to cathode, and the salt bridge completes the circuit and keeps both solutions neutral. Cell notation: Zn(s)|Zn²⁺(aq)||Cu²⁺(aq)|Cu(s). E°_cell = E°_cathode − E°_anode (right minus left). The cell reaction is spontaneous when E°_cell > 0, because ΔG° = −nFE°. The more positive E°, the stronger the oxidizing agent in that couple.

In an electrolytic cell the anode is positive (oxidation) and the cathode is negative (reduction).

• Molten NaCl gives Na and Cl₂.
• NaCl(aq) with inert electrodes gives H₂ at the cathode, and Cl₂ at the anode (O₂ if the solution is very dilute).
• CuSO₄(aq) with inert electrodes gives Cu at the cathode and O₂ at the anode, and the solution turns acidic. With Cu electrodes, the anode dissolves and Cu is deposited on the cathode (used to purify copper).

Faraday: Q = It, n(e⁻) = Q/F (F = 96 500 C mol⁻¹), and moles of product = n(e⁻)/z.

Raw materials, energy, water, transport, waste disposal, safety and the environment all decide where a plant is built. Recurring ideas: recycling unreacted materials, the counter-current principle (gas and liquid flow in opposite directions for efficient transfer, as in HNO₃ absorption) and catalysts.

Dow: seawater with Ca(OH)₂ (made from shells or limestone) precipitates Mg(OH)₂. Add HCl to get MgCl₂, dry it, and electrolyse the molten salt (700–800 °C). Mg forms at the cathode and Cl₂ at the anode, and the Cl₂ is recycled to make HCl. Membrane cell: brine is electrolysed. Cl₂ forms at the anode, and H₂ plus OH⁻ at the cathode. Only Na⁺ can pass the cation-exchange membrane, so the products are NaOH, Cl₂ and H₂.

Saponification: fat or oil (a triglyceride) + NaOH → soap (sodium salts of fatty acids) + glycerol. Adding NaCl 'salts out' the soap. In hard water, Ca²⁺ and Mg²⁺ form insoluble scum, which lowers cleaning efficiency. Biodiesel is made by transesterifying a triglyceride with methanol (NaOH catalyst), giving methyl esters and glycerol.

The raw materials are brine, limestone and ammonia (recycled). The brine is ammoniated first, then carbonated: NaCl + NH₃ + CO₂ + H₂O → NaHCO₃(s) + NH₄Cl. Heating gives 2NaHCO₃ → Na₂CO₃ + CO₂ + H₂O. NH₃ is recovered with 2NH₄Cl + Ca(OH)₂ → CaCl₂ + 2NH₃ + 2H₂O. The main by-product is CaCl₂.

• Haber–Bosch: N₂ + 3H₂ ⇌ 2NH₃, an exothermic reaction. The Resource Book gives 450–500 °C, 250–300 atm, an iron catalyst and K₂O/Al₂O₃ promoters. The temperature is a compromise between rate and yield, and unreacted gases are recycled.
• Ostwald: 4NH₃ + 5O₂ → 4NO + 6H₂O (Pt/Rh catalyst). The NO is cooled to about 150 °C: 2NO + O₂ → 2NO₂. Then 4NO₂ + O₂ + 2H₂O → 4HNO₃ is absorbed counter-currently at 5–10 atm.
• Contact process: S + O₂ → SO₂, then 2SO₂ + O₂ ⇌ 2SO₃ (V₂O₅, about 450 °C, about 1 atm, with excess air). SO₃ is absorbed into concentrated H₂SO₄ to give oleum (H₂S₂O₇), which is then diluted. SO₃ is not added directly to water because it forms an acid mist.

TiO₂ (chloride process): rutile + coke + Cl₂ at about 950 °C gives TiCl₄, which is purified by distillation and then oxidized with O₂ to pure TiO₂, regenerating Cl₂. TiO₂ is used as a white pigment. Blast furnace: the raw materials are haematite, coke, limestone and hot air. C + O₂ → CO₂; CO₂ + C → 2CO; Fe₂O₃ + 3CO → 2Fe + 3CO₂; CaCO₃ → CaO + CO₂; CaO + SiO₂ → CaSiO₃ (slag).

Addition polymers include polyethene, PVC, polystyrene, polypropene and Teflon. Condensation polymers include nylon-6,6, polyesters and Bakelite (phenol + methanal). Thermoplastics soften on heating. Thermosets have a cross-linked 3-D network and do not soften. Natural rubber is cis-polyisoprene (from 2-methylbuta-1,3-diene). Latex is coagulated with acetic or formic acid. Vulcanization with 1–3% sulfur forms S cross-links, making rubber stronger and more elastic. Ozone attacks the C=C bonds in rubber.

Ethanol by fermentation: C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂ (yeast enzymes). Vinegar: ethanol is oxidized to ethanoic acid by Acetobacter, for example from coconut toddy. Essential oils are extracted by steam distillation, solvent extraction or pressing. Examples: citronella (geraniol), cinnamon leaf (eugenol).

• Acid rain: SO₂ and NO_x form H₂SO₄ and HNO₃. Unpolluted rain is already about pH 5.6 because of CO₂.
• Global warming: CO₂, CH₄, N₂O, CFCs and water vapour absorb infrared radiation.
• Ozone layer: O₂ + UV → 2O, then O + O₂ → O₃. CFCs release Cl• in the stratosphere: Cl• + O₃ → ClO• + O₂, then ClO• + O → Cl• + O₂. HFCs contain no Cl, so they do not destroy ozone, but they are greenhouse gases.
• Photochemical smog: NO_x + volatile hydrocarbons + sunlight give O₃ and PAN. It is worst on sunny days with heavy traffic.

Water-quality parameters include dissolved oxygen (DO falls as temperature rises), BOD, COD, pH, conductivity, turbidity, hardness, nitrate and phosphate (which cause eutrophication) and heavy metals. Know which parameters matter for waste-water discharge.